A conventional bearing for radially supporting the shafts of high speed tools, such as pneumatic-motor driven orthopedic and neurosurgical tools, typically includes an inner race mounted to the supported shaft and an outer race mounted to the associated fixed housing. Because of manufacturing tolerances, the path of travel for the roller members,, which interconnect the races, do not define a true circle, even in high precision bearings. In fact, the roller members meander randomly from the ideal circular orbit between the inner and outer races. Also, because of manufacturing tolerances and assembly requirements, there may be play between the outer race and the supporting housing as well as between the inner race and the supported shaft. Consequently, radial motion of the tool shaft is permitted, allowing vibration and chatter. At the high rotational speeds of pneumatically driven surgical tools, such vibrations are unacceptable and in some circumstances can result in catastrophic failure. Accordingly, rotational speeds for such high speed surgical tools have been typically limited to less than 80,000 RPM.